We want to select from a set of hash functions H with reasonable certainty that the above property is true.

Thus, the number of functions f in H such that h(x) = h(y) for
x,y U must satisfy

**Definition:** A *H*|/*m* hash functions such that h(x) = h(y)
for x,y U.

where key x = <

a = <

is a universal collection of hash functions.

Thus, we want to randomly select ``a'' each time.